TY - JOUR

T1 - Noisy monitored quantum dynamics of ergodic multi-qubit systems

AU - Schomerus, Henning

PY - 2022/5/27

Y1 - 2022/5/27

N2 - I employ random-matrix methods to set up and solve statistical models of noisy nonunitary dynamics that appear in the context of monitored quantum systems. The models cover a range of scenarios combining random dynamics and measurements of variable strength of one or several qubits. The combined dynamics drive the system into states whose statistics reflect the competition of randomizing unitary evolution and the measurement-induced backaction collapsing the state. These effects are mediated by entanglement, as I describe in detail by analytical results. For the paradigmatic case of monitoring via a single designated qubit, this reveals a simple statistical mechanism, in which the monitoring conditions the state of the monitored qubit, which then imposes statistical constraints on the remaining quantities of the system. For the case of monitoring several qubits with prescribed strength, the developed formalism allows one to set up the statistical description and solve it numerically. Finally, I also compare the analytical results to the monitored dynamics of a quantum kicked top, revealing two regimes where the statistical model either describes the full stationary dynamics, or resolves time scales during particular parts of the evolution.

AB - I employ random-matrix methods to set up and solve statistical models of noisy nonunitary dynamics that appear in the context of monitored quantum systems. The models cover a range of scenarios combining random dynamics and measurements of variable strength of one or several qubits. The combined dynamics drive the system into states whose statistics reflect the competition of randomizing unitary evolution and the measurement-induced backaction collapsing the state. These effects are mediated by entanglement, as I describe in detail by analytical results. For the paradigmatic case of monitoring via a single designated qubit, this reveals a simple statistical mechanism, in which the monitoring conditions the state of the monitored qubit, which then imposes statistical constraints on the remaining quantities of the system. For the case of monitoring several qubits with prescribed strength, the developed formalism allows one to set up the statistical description and solve it numerically. Finally, I also compare the analytical results to the monitored dynamics of a quantum kicked top, revealing two regimes where the statistical model either describes the full stationary dynamics, or resolves time scales during particular parts of the evolution.

KW - General Physics and Astronomy

KW - Mathematical Physics

KW - Modeling and Simulation

KW - Statistics and Probability

KW - Statistical and Nonlinear Physics

U2 - 10.1088/1751-8121/ac6320

DO - 10.1088/1751-8121/ac6320

M3 - Journal article

VL - 55

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 21

M1 - 214001

ER -